\(R_n=\left\lbrace \left[\begin{array}{lccccr}a & a_{12} & \dots & a_{1(n-1)} & a_{1n}\\0 & a & \dots & a_{2(n-1)} & a_{2n}\\\vdots & \vdots &\ddots & \vdots & \vdots \\0 & 0 & \dots & a &a_{(n-1)n}\\0 & 0 & \dots & 0 & a \\\end{array}\right]|a, a_{ij}\in R,~ i<j\right\rbrace \) 
is semicommutative whenever \(R\)  is reduced and \(n=3\) . However, \(R_n\)  is not semicommutative for \(n\ge 4\)  even if \(R\)  is reduced (see [1]}). So one might suspect whether \(R_n\)  is pointwise semicommutative for \(n\ge 4\)  whenever \(R\)  is reduced. Nevertheless, the following example obliterates the possibility.
